This invention relates generally to the field of measuring the viscosity of liquids, and more particularly, to a method of isolating the surface tension and yield stress effects when determining the viscosity of a liquid using a U-shaped scanning capillary tube viscometer.
In a scanning capillary tube viscometer, a U-shaped tube is used where one portion of the U-shaped tube is formed by a flow restrictor, e.g., capillary tube. One leg of the U-shaped tube supports a falling column of fluid and the other leg supports a rising column of fluid Furthermore, movement of either one or both of these columns is monitored, hence the term xe2x80x9cscanning.xe2x80x9d See FIG. 1. It should be understood that the term xe2x80x9cscanning,xe2x80x9d as used in this Specification, also includes the detection of the change in mass (e.g., weight) in each of the columns. Thus, all manners of detecting the change in the column mass, volume, height, etc. is covered by the term xe2x80x9cscanning.xe2x80x9d
In order to measure liquid viscosity using a U-shaped scanning capillary tube viscometer, the pressure drop across the capillary tube has to be precisely estimated from the height difference between the two fluid columns in the respective legs of the U-shaped tube. However, under normal circumstances, the height difference, xcex94h(t), contains the effects of surface tension and yield stress. Therefore, the contributions of the surface tension (xcex94hst) and yield stress (xcfx84y) to xcex94h(t), have to be taken into account, or isolated. Here, xcex94h(t) is equal to h1(t)xe2x88x92h2(t).
The magnitude of the surface tension of a liquid in a tube differs greater depending on the condition of the tube wall. Normally, the surface tension reported in college textbooks are measured from a perfectly wet tube. However, in reality, the falling column has a perfectly wet surface while the rising column has a perfectly dry surface. When the tube is completely dry, the value of the surface tension from the same tube can be substantially different from that measured from a perfectly wet tube. Hence, there is a pronounced effects of the surface tension on the overall height difference between the two columns. The height difference caused by the surface tension can be significantly greater than the experimental resolution required for the accuracy of viscosity measurement. For example, the difference between surface tensions of two columns in the U-shaped tube can produce the height difference, xcex94hst, of 3.5 mm where the height difference, xcex94h (t), must be measured as accurately as 0.1 mm. Thus, it is extremely important to isolate the effect of the surface tension from the viscosity measurement.
Similarly, the effect of yield stress, xcfx84y, must be isolated from the viscosity measurement.
Thus, there remains a need for accounting for, or isolating, the surface tension and yield stress in viscosity measurements when using a scanning capillary tube viscometer.
A method for isolating the effect of surface tension on a fluid that is flowing in a U-shaped tube having a flow restrictor (e.g., a capillary tube) forming a portion of said U-shaped tube. The fluid forms a falling column of fluid, having a first height that changes with time, in a first leg of the U-shaped tube and a rising column of fluid, having a second height that changes with time, in a second leg of said U-shaped tube. The method comprises the steps of: (a) detecting the difference between the first and second heights over time; and (b) subtracting a term representing surface tension from the difference.
A method of isolating the effect of surface tension on a fluid and the effect of yield stress of a fluid that is flowing in a U-shaped tube having a flow restrictor forming a portion of said U-shaped tube. The fluid forms a falling column of fluid, having a first height that changes with time, in a first leg of said U-shaped tube and a rising column of fluid, having a second height that changes with time, in a second leg of said U-shaped tube. The method comprises the steps of: (a) detecting the difference between the first and second heights over time for generating falling column data and rising column data; (b) curve fitting an equation using the falling column data and the rising column data to determine: (1) a term representing surface tension; and (2) a term representing the yield stress.